Back when Typo Knig was in graduate school, we took 4 weeks off and did a cross-country drive. More of a triangle than a square, as we started and ended in North Carolina. Overall, about 8,000 miles on the car.
I’d say your timing would depend on your goals for the trip. Do you want to see natural wonders? big cities? In our case, we were more into natural wonders, and timed our driving accordingly - concentrating on heavy driving day(s) interrupted by longer stops in a location. For example, we spent 3 solid days driving from NC to Colorado Springs, then spent time there; another long driving day to Grand Teton National Park and a few days there, 2 long driving days to Seattle then some time there… 3 days driving down the west coast (camping along the way) - that was probably the only part where we combined scenery with driving . A few days in Berkeley, then we hit the road and had nearly 5 solid driving days to get home, with stops each night to sleep in a hotel. I’m still sorta kicking myself for being within 50 miles of the Grand Canyon when heading east on I-40, and NOT taking the side trip, but we were “sceneried out” by then (we did visit the GC nearly 20 years later).
All in all, I’d estimate 160 hours of driving, since we tended to average 50 mph when factoring in stops etc.
Our heavy driving days tended to be 12-14 hours.
Consider your vehicle. We did it in a Mazda 626 sedan (with a cartop carrier for tent etc.). You might consider renting a minivan or something - more luggage space, more legroom, more space for stuff like a big cooler. Having lunch “on board” saves a lot of travel time (we kept sandwich fixings etc.). It’s 33 years later and we still have our big cooler!
Another thing we did was to have only soft-sided luggage (duffels etc.). That way we could have all our clean stuff in one bag and put the dirty clothing in another bag. The clean bag would compress as the dirty bag grew, so they took up the same amount of space in the car. I’m sure we did laundry en route, at some point, but I honestly don’t remember where or when. I do remember that in Grand Teton, we had to drive 10 miles or so to another campground to shower, LOL.
Your particular route would be eminently doable by train - there are several ways to get from New York to Chicago, thence from Chicago to Seattle, then down the west coast, then across the southern part of the US. There are two trains daily that go from Florida up to NYC. You’d want to make sure to allow for stopovers of several days in various places, then you’d need to arrange for rental car etc. there. On-train accommodations are worth looking into - they add a fair bit to the cost but you’d feel MUCH better on arrival if you’ve gotten some lying-down sleep time.
An RV rental might be an option, depending on your trip goals. It won’t save you money over hotels / trains / driving, but it will give you the convenience of not having to trek luggage into hotels, and you can stop wherever you like for a bit of rest.
